Questions
BUOYANCY, FLOATATION, AND ACCELERATED FLUID MASSES
1. A body is weighed twice while put off in two different fluids of
specific gravities 0.85 and 1.6. If the balance readings are 30 and 18 kg.
Find the density of the body.
2. A cylinder has a specific gravity of 0.95 and a length of 80 cm floats with
its axis vertical in a vessel comprising an oil of specific gravity 0.84
and water. If we want the cylinder to become totally immersed, what
should be the minimum depth of oil required to fulfil this condition.
3. A rectangular tank has dimensions 120 x 66 x 60 cm and weighs 1410
N. If the tank is permitted to float in freshwater, will the equilibrium be
firm when the 60 cm edge is vertical?
4. A hollow opened wooden cylinder of specific gravity 0.60 has an outer
diameter of 0.80 m, an inner diameter of 0.40 m. It is required to float
this cylinder in oil of specific gravity o f 0.85. Calculate the maximum
height of the cylinder, w h i c h keeps it floating with its axis vertical.
5. For the floating unit shown in Fig. (1) It is required to check its stability.
6. A rectangular buoy 10.3 m long, 7.3 m wide, and 2.4 m deep have a
displacement weight of 74 tons. If an empty cylindrical boiler weighs 70
tons of 5.5m diameter and 10.3 m long is attached to its deck, check
the stability of the system while floating in seawater (1.03), when the
boiler's axis is: a) horizontal (parallel to buoy axis), b) vertical.
7. An open rectangular tank is 2 m long, 1 m wide, and 1.5 m deep. If
the tank encloses gasoline to a depth of 1 m. F i n d t h e maximum
horizontal acceleration with which the tank can move without spilling
any gasoline. Find a l s o the amount of retained gasoline in the tank
when it is accelerated at double the previous value.
8. A locked rectangular tank 1.2 m high, 2.5 m long, and 1.5 wide is
filled with water. If we raise the pressure at the top of the tank to 60
KN/m2, find the pressure at the corners of this tank when it is
2
decelerated horizontally alongside the direction of its length at 5 m / s .
Find the forces on both ends of the tank and use Newton’s law to find
their difference.
9. A closed rectangular tank 6 m long, 2 m wide, and 2 m deep is partly
filled with oil (0.9) to a depth of 1.5 m under a pressure of 0.4 bar.
Calculate the maximum acceleration with which the tank can move in
the direction of its
1
, length if we fix a safety valve that bears a maximum pressure of 60
2
KN/m at the center of its back end.
10. In problem 11, find the force on the bottom side of the tank when it
moves with the same acceleration, but in the vertical direction: a)
upwards, b) downwards.
11. A closed cubic box of side 2.0 m contains water to a depth of 1.0 m.
Find the pressure force on both t h e top and bottom sides of the tank if
2
it moves with a horizontal acceleration of 1 9 . 6 m/s . Draw the water
surface and the pressure distributions on the four sides of the cube.
12. An opened cylinder with a height of 375 mm, 150 mm diameter is filled with
water and revolved about its vertical axis at an angular speed of 33.5
rad/s. Find the depth of water in the cylinder when comes to rest. If the
speed is doubled, find the volume of water that remains in the cylinder.
13. A cylindrical tank of 1.0 m diameter, 2.0 m height contains water to a
depth of 1.5 m. if the tank is rotated around its vertical axis, what is the
range of the angular velocity (ω) that would cause spilling of water but
would not uncover the base?
14. A closed cylindrical tank 2 m long, 1 m diameter is partially filled with
water to 1.5 m depth.
The pressure at the water surface is 40 KN/m2. If the tank is rotated
about its vertical axis with an angular velocity of 12 rad/s, find the pressure at
the bottom of the tank; at its center, and edge. Also, find the force on the top
of the tank.
15. A locked cylindrical tank 2 m high and 1 m diameter is occupied
2
with glycerin (1.25) under a pressure of 2 t/m . The tank is revolved about
its vertical axis at a rate of 2000 rpm. If the top plate of the tank is linked to
the cylinder by rivets that bear a force of 50 KN, find the number of rivets
required to hold the top plate to the cylinder.
Fig. (1)
2
BUOYANCY, FLOATATION, AND ACCELERATED FLUID MASSES
1. A body is weighed twice while put off in two different fluids of
specific gravities 0.85 and 1.6. If the balance readings are 30 and 18 kg.
Find the density of the body.
2. A cylinder has a specific gravity of 0.95 and a length of 80 cm floats with
its axis vertical in a vessel comprising an oil of specific gravity 0.84
and water. If we want the cylinder to become totally immersed, what
should be the minimum depth of oil required to fulfil this condition.
3. A rectangular tank has dimensions 120 x 66 x 60 cm and weighs 1410
N. If the tank is permitted to float in freshwater, will the equilibrium be
firm when the 60 cm edge is vertical?
4. A hollow opened wooden cylinder of specific gravity 0.60 has an outer
diameter of 0.80 m, an inner diameter of 0.40 m. It is required to float
this cylinder in oil of specific gravity o f 0.85. Calculate the maximum
height of the cylinder, w h i c h keeps it floating with its axis vertical.
5. For the floating unit shown in Fig. (1) It is required to check its stability.
6. A rectangular buoy 10.3 m long, 7.3 m wide, and 2.4 m deep have a
displacement weight of 74 tons. If an empty cylindrical boiler weighs 70
tons of 5.5m diameter and 10.3 m long is attached to its deck, check
the stability of the system while floating in seawater (1.03), when the
boiler's axis is: a) horizontal (parallel to buoy axis), b) vertical.
7. An open rectangular tank is 2 m long, 1 m wide, and 1.5 m deep. If
the tank encloses gasoline to a depth of 1 m. F i n d t h e maximum
horizontal acceleration with which the tank can move without spilling
any gasoline. Find a l s o the amount of retained gasoline in the tank
when it is accelerated at double the previous value.
8. A locked rectangular tank 1.2 m high, 2.5 m long, and 1.5 wide is
filled with water. If we raise the pressure at the top of the tank to 60
KN/m2, find the pressure at the corners of this tank when it is
2
decelerated horizontally alongside the direction of its length at 5 m / s .
Find the forces on both ends of the tank and use Newton’s law to find
their difference.
9. A closed rectangular tank 6 m long, 2 m wide, and 2 m deep is partly
filled with oil (0.9) to a depth of 1.5 m under a pressure of 0.4 bar.
Calculate the maximum acceleration with which the tank can move in
the direction of its
1
, length if we fix a safety valve that bears a maximum pressure of 60
2
KN/m at the center of its back end.
10. In problem 11, find the force on the bottom side of the tank when it
moves with the same acceleration, but in the vertical direction: a)
upwards, b) downwards.
11. A closed cubic box of side 2.0 m contains water to a depth of 1.0 m.
Find the pressure force on both t h e top and bottom sides of the tank if
2
it moves with a horizontal acceleration of 1 9 . 6 m/s . Draw the water
surface and the pressure distributions on the four sides of the cube.
12. An opened cylinder with a height of 375 mm, 150 mm diameter is filled with
water and revolved about its vertical axis at an angular speed of 33.5
rad/s. Find the depth of water in the cylinder when comes to rest. If the
speed is doubled, find the volume of water that remains in the cylinder.
13. A cylindrical tank of 1.0 m diameter, 2.0 m height contains water to a
depth of 1.5 m. if the tank is rotated around its vertical axis, what is the
range of the angular velocity (ω) that would cause spilling of water but
would not uncover the base?
14. A closed cylindrical tank 2 m long, 1 m diameter is partially filled with
water to 1.5 m depth.
The pressure at the water surface is 40 KN/m2. If the tank is rotated
about its vertical axis with an angular velocity of 12 rad/s, find the pressure at
the bottom of the tank; at its center, and edge. Also, find the force on the top
of the tank.
15. A locked cylindrical tank 2 m high and 1 m diameter is occupied
2
with glycerin (1.25) under a pressure of 2 t/m . The tank is revolved about
its vertical axis at a rate of 2000 rpm. If the top plate of the tank is linked to
the cylinder by rivets that bear a force of 50 KN, find the number of rivets
required to hold the top plate to the cylinder.
Fig. (1)
2
